Probability Calculator

Probability = number of favorable outcomes / total possible outcomes. For rolling a 6 on a die: P = 1/6 = 0.1667 = 16.67%. Probability always ranges from 0 (impossible) to 1 (certain). Enter outcomes as fractions, decimals, or percentages and the calculator converts between all formats.

For independent events: P(A and B) = P(A) x P(B). Flipping heads AND rolling a 6: (1/2) x (1/6) = 1/12. For dependent events: P(A and B) = P(A) x P(B|A), where P(B|A) is the probability of B given A has occurred. The calculator handles both cases.

P(A or B) = P(A) + P(B) - P(A and B). The subtraction prevents double-counting outcomes that satisfy both events. For mutually exclusive events (no overlap), simply add: P(A or B) = P(A) + P(B). Rolling a 3 or 5 on a die: 1/6 + 1/6 = 2/6 = 1/3.

The complement of an event is everything that is not that event. P(not A) = 1 - P(A). This is useful when the "not" probability is easier to calculate. For example, the probability of rolling at least one 6 in 4 rolls = 1 - P(no sixes) = 1 - (5/6)^4 = 0.5177 = 51.77%.

Conditional probability P(B|A) is the probability of B given that A has already occurred. P(B|A) = P(A and B) / P(A). For example, if a bag has 3 red and 2 blue balls, P(2nd red | 1st red) = 2/4 = 0.5, because after drawing one red ball, 2 of the remaining 4 are red.